Quantum tunneling and scattering of a composite object reexamined

Abstract

This work presents an extensive exploration of scattering and tunneling involving composite objects with intrinsic degrees of freedom. We aim at exact solutions to such scattering problems. Along this path we demonstrate solution to model Hamiltonians, and develop different techniques for addressing these complex reaction-physics problems, discuss their applicability, and investigate the relevant convergence issues. As examples, we study the scattering of a two-constituent deuteronlike systems either with an infinite set of intrinsic bound states or with a continuum of states that allows for breakup. We show that the internal degrees of freedom of the projectile and its virtual excitation in the course of reactions play an important role in shaping the S-matrix and related observables, giving rise to enhanced or reduced tunneling in various situations.

Applicability of the continuum-discretized coupled-channels method to the deuteron breakup at low energies

“…In conclusion, we have demonstrated the applicability of CDCC to elastic breakup reactions 10 Be(d, pn) 10 Be at E d = 21 MeV and 12 C(d, pn) 12 C at E d = 12 MeV, by confirming the convergence of the CDCC model space with respect to k max . As a next step, a more systematic investigation on the role of closed channels, in transfer reactions in particular, will be important.…”

“…This has numerically been confirmed in Ref. [12] for a one-dimensional scattering problem, and in Ref. [13] for the scattering of 11 Be.…”

“…2 the results for 12 C at E d = 56 MeV. For this reaction, no significant difference between CDCC and FAGS was reported in Ref.…”

“…We use ∆k = 0.05 fm −1 and ℓ max = 8 for all the calculation shown below. As for k max , we take 0.9 fm −1 for 12 C(d, pn) 12 C at E d = 12 MeV (Fig. 1) and 1.1 fm −1 for other two reactions (Figs.…”

“…In the multipole expansion of the nucleon-nucleus optical potential, we take the multipolarities λ up to 16; it turned out that the multipoles for λ > 8 have no effect on the results shown below. Figure 1(a) shows the angular distribution of the deuteron breakup cross section on 12 C at E d = 12 MeV integrated over the p-n breakup energy ǫ. The horizontal axis is the scattering angle θ of the center-of-mass of the p-n system.…”